The Tarskian Turn: Deflationism and Axiomatic Truth

2. Axiomatic Theories of Truth

2 Axiomatic Theories of Truth In this chapter, contemporary theories of truth will first be distinguished from more traditional, substantial truth theories. Subsequently, a distinction is drawn, within contemporary theories, between semantic and axiomatic approaches. It will be argued that the axiomatic approach ought to be preferred over the semantic approach. Thus we will acquire a strong motivation for embarking on a search for adequate axiomatic theories of truth. 2.1 Pilate’s Question What is truth? (John 18:38) The philosophical debate about truth was dominated until recently by deep and substantial theories of truth. No attempt is made here to do justice to the complexity of these theories. We content ourselves here with briefly rehearsing the central tenets of some of the most influential deep theories of truth. This provides the contrasting background against which deflationist views about truth are formulated. The correspondence theory of truth This is one of the oldest deep theories of truth. Some trace it all the way back to the work of Aristotle. However, Aristotle ’s remarks on the matter seem too cryptic to label him with much confidence as the first card-carrying correspondence theorist. The correspondence theory does find a fairly clear expression in the work of Thomas Aquinas, who writes [Aquinas 1981, Ia, Q.16]: Further, Isaac says in his book On Definitions that truth is the equation of thought and thing. Now just as the intellect with regard to complex things can be equated to things, so also with regard to simple things; and this is true also of sense apprehending a thing as it is. 12 Chapter 2 Modern correspondence theorists no longer take things to correspond to true propositions; they consider facts to be the truthmakers of propositions:1 A proposition is true if and only if it corresponds with a fact that makes it true. The coherence theory of truth The roots of the coherence theory of truth can be traced back to certain versions of German idealism. The coherence theory takes the primary truth-bearers to be theoretical wholes rather than propositions. Its central idea is: A theory is true if and only if it is coherent. A modern-day expression of the coherence theory of truth can be found in the works of Nicholas Rescher.2 Peirce’s anti-realist theory Peirce expresses his anti-realist view by equating truth with “[t]heopinionwhichisfatedtobeultimatelyagreedbyallwhoinvestigate"[Peirce 1978, 5.407]. Thus, according to the pragmatic theory of truth, there is an intimate connection between truth and knowledge. In a nutshell: A hypothesis is true if and only if it is known in the ideal limit. The pragmatic theory William James succinctly expresses the core of the pragmatic view [James 1907, p. 59]: The essential thing is the process of being guided. Any idea that helps us to deal, whether practically or intellectually, with either the reality or its belongings, that doesn’t entangle our progress in frustrations, that fits, in fact, and adapts our life to the reality’s whole setting, will agree sufficiently to meet the requirement. It will hold true of that reality. So according to the pragmatic theory of truth, there is an intimate connection between truth and usefulness. In a nutshell: A theory is true if and only if it is practical. There are prima facie objections to most of these theories. They may or may not in the end be decisive, but they are reasonable concerns. 1. For more about present-day truthmaker theories, see [Armstrong 2004] and [Beebee & Dodd 2005]. 2. See [Rescher 1982]. Axiomatic Theories of Truth 13 The coherence theory of truth at first sight seems too liberal: It is hard to see why there can be only one systematic whole that is coherent. Indeed, it seems that there can be more than one such systematic wholes, which, while being internally coherent, contradict each other, and thus cannot all be true. Therefore, coherence appears to be a necessary condition for truth, but not a sufficient one. Peirce’s anti-realist theory of truth is a verificationist theory. Truth is judged to be an epistemic notion. But truth is not a wholly epistemic notion, it seems. Whether a judgment is true depends solely on the meaning of the words out of which the judgment is composed and the way things are. Especially this last factor is independent of the evidence that...